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Emergence of Cosmic Space with a General Form of The Entropy

An emergence of cosmic space has been suggested by Padmanabhan in [arXiv:1206.4916]. This new interesting approach argues that the expansion of the universe is due to the difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. In this paper, we derive, using emergence of cosmic space framework, the general dynamical equation of FRW universe filled with a perfect fluid by considering a generic form of the entropy as a function of area. Our derivation is considered as a generalization of emergence of cosmic space with a general form of entropy. We then apply our derived equation with the corrected entropy-area law that follows from Generalized Uncertainty Principle (GUP) and derive a modified Friedmann equations due to the GUP. We got a dynamical equation of FRW universe subject to the Hubble parameter has a maximal bound related to the Planck scale. This might possibly introduce a natural cutoff on the Hubble parameter, and hence a possible resolution for the Big Bang Singularity.